相关论文: Convexity and the Separability Problem of Quantum …
Quantum entanglement is a key resource in quantum computing and quantum information processing tasks. However, its quantification remains a major challenge since it cannot be directly extracted from physical observables. To address this…
We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an…
Motivated by the separability problem in quantum systems $2\otimes4$, $3\otimes3$ and $2\otimes2\otimes2$, we study the maximal (proper) faces of the convex body, $S_1$, of normalized separable states in an arbitrary quantum system with…
We consider four norms on tensor product spaces that have appeared in quantum information theory and demonstrate duality relationships between them. We show that the product numerical radius is dual to the robustness of entanglement, and we…
A discrimination problem consists of $N$ linearly independent pure quantum states $\Phi=\{\ket{\phi_i}\}$ and the corresponding occurrence probabilities $\eta=\{\eta_i\}$. To any such problem we associate, up to a permutation over the…
Quantifying quantum entanglement is a pivotal challenge in quantum information science, particularly for high-dimensional systems, due to its computational complexity. This thesis extends the geometric measure of entanglement (GME) to…
We derive an exact uncertainty relation for arbitrary quantum states of finite-dimensional Hilbert spaces. For any given $k$-partition of a $d$-dimensional multipartite system, we introduce the total uncertainty as the sum of the…
For a random quantum state on $H=C^d \otimes C^d$ obtained by partial tracing a random pure state on $H \otimes C^s$, we consider the whether it is typically separable or typically entangled. For this problem, we show the existence of a…
Macroscopic quantum phenomena refer to quantum features in objects of `large' sizes, systems with many components or degrees of freedom, organized in ways where they can be identified as macroscopic objects. This emerging field is ushered…
Characterizing the entanglement of matrix degrees of freedom is essential for understanding the holographic emergence of spacetime. The Quantum Hall Matrix Model is a gauged $U(N)$ matrix quantum mechanics with two matrices whose ground…
The `operator entanglement' of a quantum operator $O$ is a useful indicator of its complexity, and, in one-dimension, of its approximability by matrix product operators. Here we focus on spin chains with a global $U(1)$ conservation law,…
We report the creation of a wide range of quantum states with controllable degrees of entanglement and entropy using an optical two-qubit source based on spontaneous parametric downconversion. The states are characterised using measures of…
For multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parameterization obtained by the juxtaposition of the affine Bloch vectors of each qubit. While it maintains the tensorial structure of the underlying space, it…
Very often, in the course of uncertainty quantification tasks or data analysis, one has to deal with high-dimensional random variables (RVs). A high-dimensional RV can be described by its probability density (pdf) and/or by the…
The Separability Problem is approached from the perspective of Ellipsoidal Classification. A Density Operator of dimension N can be represented as a vector in a real vector space of dimension $N^{2}- 1$, whose components are the projections…
Measurements destroy entanglement. Building on ideas used to study `quantum disentangled liquids', we explore the use of this effect to characterize states of matter. We focus on systems with multiple components, such as charge and spin in…
Quantum measurements are inherently noisy, hindering reliable entanglement detection and limiting the scalability of quantum technologies. While error mitigation and correction strategies exist, they often impose prohibitive resource…
Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly…
Quantum entanglement of mechanical systems emerges when distinct objects move with such a high degree of correlation that they can no longer be described separately. Although quantum mechanics presumably applies to objects of all sizes,…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…